Add Generate Parentheses algorithm in TypeScript (#166)

* Add Generate Parentheses algorithm in TypeScript

* Fix typo

---------

Co-authored-by: IcarusTheFly <IcarusTheFly@users.noreply.github.com>
Co-authored-by: Lars Müller <34514239+appgurueu@users.noreply.github.com>

Author: IcarusTheFly

backtracking/generateParentheses.ts

@@ -0,0 +1,31 @@
+/**
+ * Given a number n pairs of parentheses, generate all combinations of valid parentheses
+ * @param {number} n: Number of given parentheses
+ * @return {string[]} result: Array that contains all valid parentheses
+ * @see https://leetcode.com/problems/generate-parentheses/
+ */
+
+const generateParentheses = (n: number): string[] => {
+  const result: string[] = [];
+
+  const solve = (chars: string, openParentheses: number, closedParentheses: number) => {
+    if (openParentheses === n && closedParentheses === n) {
+      result.push(chars);
+      return;
+    }
+
+    if (openParentheses <= n) {
+      solve(chars + "(", openParentheses + 1, closedParentheses);
+    }
+
+    if (closedParentheses < openParentheses) {
+      solve(chars + ")", openParentheses, closedParentheses + 1);
+    }
+  };
+
+  solve("", 0, 0);
+
+  return result;
+};
+
+export { generateParentheses };

backtracking/test/generateParentheses.test.ts

@@ -0,0 +1,83 @@
+import { generateParentheses } from "../generateParentheses";
+
+const cases: [number, string[]][] = [
+  [0, [""]],
+  [1, ["()"]],
+  [2, ["(())", "()()"]],
+  [3, ["((()))", "(()())", "(())()", "()(())", "()()()"]],
+  [
+    4,
+    [
+      "(((())))",
+      "((()()))",
+      "((())())",
+      "((()))()",
+      "(()(()))",
+      "(()()())",
+      "(()())()",
+      "(())(())",
+      "(())()()",
+      "()((()))",
+      "()(()())",
+      "()(())()",
+      "()()(())",
+      "()()()()",
+    ],
+  ],
+  [
+    5,
+    [
+      "((((()))))",
+      "(((()())))",
+      "(((())()))",
+      "(((()))())",
+      "(((())))()",
+      "((()(())))",
+      "((()()()))",
+      "((()())())",
+      "((()()))()",
+      "((())(()))",
+      "((())()())",
+      "((())())()",
+      "((()))(())",
+      "((()))()()",
+      "(()((())))",
+      "(()(()()))",
+      "(()(())())",
+      "(()(()))()",
+      "(()()(()))",
+      "(()()()())",
+      "(()()())()",
+      "(()())(())",
+      "(()())()()",
+      "(())((()))",
+      "(())(()())",
+      "(())(())()",
+      "(())()(())",
+      "(())()()()",
+      "()(((())))",
+      "()((()()))",
+      "()((())())",
+      "()((()))()",
+      "()(()(()))",
+      "()(()()())",
+      "()(()())()",
+      "()(())(())",
+      "()(())()()",
+      "()()((()))",
+      "()()(()())",
+      "()()(())()",
+      "()()()(())",
+      "()()()()()",
+    ],
+  ],
+];
+
+describe("Generate Parentheses", () => {
+  test.each(cases)(
+    "generate all valid parentheses of input %n",
+    (n: number, expected: string[]) => {
+      expect(generateParentheses(n)).toStrictEqual(expected);
+    }
+  );
+});